The dark state of a three-core waveguide was adapted to study the influence of the nonlinearity on the coherent population trapping (CPT) by Silberberg, etc. However, the numerical result of such a waveguide shows that both the CPT and nonlinear self-trapping can result in the dark states. When both effects occur, the dark states will be destroyed. Thus the destruction of dark states are due to the both effects, which means one cannot simply attribute the disappearance of darks states to the CPT solely. In the ideal CPT case, the critical power of nonlinearity approaches to infinity, which means that the nonlinearity of the system does not influence the ideal CPT quantum effects.